Rental or loaner car coverage is contractual meaning if you bought the coverage, you are entitled to it per your insurance policy contract. As to the other driver, it is a liability question and if the other driver's insurance company admits or settles on liability part of the settlement will most likely take some alternate transportation but if your insurer has paid you under your policy it is entitled to recoup what it paid you from the at fault driver's insurer -- that's called subrogation.
I am not admitted in Ill. (only in CA), so I can only provide a sort of general response. In general, one measure of the loss you can claim as a result another's negligence is for loss of use of your property. Thus, if you get a rental car, the other person's insurance should have to reimburse you the reasonable costs of that rental. That is why carriers often agree to provide a rental, through companies with which they have financial arrangements for lower costs. I'd contact the other person's carrier right away.
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